LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-09-21T01:57:27.139948

Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
abelian_quotient	text
all_subgroups_known	boolean
almost_simple	boolean
aut_abelian	boolean
aut_cyclic	boolean
aut_derived_length	smallint
aut_exponent	numeric
aut_gen_orders	numeric[]
aut_gens	numeric[]
aut_group	text
aut_hash	bigint
aut_nilpotency_class	smallint
aut_nilpotent	boolean
aut_order	numeric
aut_permdeg	integer
aut_perms	numeric[]
aut_phi_ratio	double precision
aut_solvable	boolean
aut_stats	numeric[]
aut_supersolvable	boolean
aut_tex	text
autcent_abelian	boolean
autcent_cyclic	boolean
autcent_exponent	numeric
autcent_group	text
autcent_hash	bigint
autcent_nilpotent	boolean
autcent_order	numeric
autcent_solvable	boolean
autcent_split	boolean
autcent_supersolvable	boolean
autcent_tex	text
autcentquo_abelian	boolean
autcentquo_cyclic	boolean
autcentquo_exponent	numeric
autcentquo_group	text
autcentquo_hash	bigint
autcentquo_nilpotent	boolean
autcentquo_order	numeric
autcentquo_solvable	boolean
autcentquo_supersolvable	boolean
autcentquo_tex	text
cc_stats	numeric[]
center_label	text
center_order	numeric
central_product	boolean
central_quotient	text
commutator_count	integer
commutator_label	text
complements_known	boolean
complete	boolean
complex_characters_known	boolean
composition_factors	text[]
composition_length	smallint
conjugacy_classes_known	boolean
counter	integer
cyclic	boolean
derived_length	smallint
dihedral	boolean
direct_factorization	jsonb
direct_product	boolean
div_stats	numeric[]
element_repr_type	text
elementary	integer
eulerian_function	numeric
exponent	numeric
exponents_of_order	smallint[]
factors_of_aut_order	integer[]
factors_of_order	smallint[]
faithful_reps	numeric[]
familial	boolean
frattini_label	text
frattini_quotient	text
hash	bigint
hyperelementary	integer
inner_abelian	boolean
inner_cyclic	boolean
inner_exponent	numeric
inner_gen_orders	numeric[]
inner_gens	numeric[]
inner_hash	bigint
inner_nilpotent	boolean
inner_order	numeric
inner_split	boolean
inner_tex	text
inner_used	smallint[]
irrC_degree	integer
irrQ_degree	integer
irrQ_dim	integer
irrR_degree	integer
irrep_stats	numeric[]
label	text
linC_count	numeric
linC_degree	integer
linFp_degree	integer
linFq_degree	integer
linQ_degree	integer
linQ_degree_count	numeric
linQ_dim	integer
linQ_dim_count	numeric
linR_count	numeric
linR_degree	integer
maximal_subgroups_known	boolean
metabelian	boolean
metacyclic	boolean
monomial	boolean
name	text
ngens	smallint
nilpotency_class	smallint
nilpotent	boolean
normal_counts	integer[]
normal_index_bound	numeric
normal_order_bound	numeric
normal_subgroups_known	boolean
number_autjugacy_classes	integer
number_characteristic_subgroups	integer
number_conjugacy_classes	integer
number_divisions	integer
number_normal_subgroups	integer
number_subgroup_autclasses	integer
number_subgroup_classes	integer
number_subgroups	numeric
old_label	text
order	numeric
order_factorization_type	integer
order_stats	numeric[]
outer_abelian	boolean
outer_cyclic	boolean
outer_equivalence	boolean
outer_exponent	numeric
outer_gen_orders	numeric[]
outer_gen_pows	numeric[]
outer_gens	numeric[]
outer_group	text
outer_hash	bigint
outer_nilpotent	boolean
outer_order	numeric
outer_permdeg	integer
outer_perms	numeric[]
outer_solvable	boolean
outer_supersolvable	boolean
outer_tex	text
pc_rank	smallint
perfect	boolean
permutation_degree	integer
pgroup	smallint
primary_abelian_invariants	integer[]
quasisimple	boolean
rank	smallint
rational	boolean
rational_characters_known	boolean
ratrep_stats	numeric[]
representations	jsonb
schur_multiplier	integer[]
semidirect_product	boolean
simple	boolean
smith_abelian_invariants	integer[]
solvability_type	smallint
solvable	boolean
subgroup_inclusions_known	boolean
subgroup_index_bound	numeric
supersolvable	boolean
sylow_subgroups_known	boolean
tex_name	text
transitive_degree	integer
wreath_data	text[]
wreath_product	boolean

gps_groups • Show schema

{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 10230, 'aut_gen_orders': [31, 3, 5], 'aut_gens': [[589826, 1057], [261591, 951644], [286104, 943581], [959760, 1004447]], 'aut_group': '163680.a', 'aut_hash': 6491569111290142452, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 163680, 'aut_permdeg': 992, 'aut_perms': [241663516454389007025133014463400093234847836436477082667613179117701610532545843696304799464005406403175804788560405080446682531568326356771828470580924869813461304122840140790132888311274447821286886676947568047241617531284647745143171986266800292482647018957411310696618438316914372196514225204689432767608889642409984333457316785666547676501668876822866820984881124631232881534936635736694956037380205593203701030996756381684584550842705179980838709051652043959481564267288121423353658598189045983534451052036158023486208122205446479198857603293194171584297121155195609054047364794778502797733847217629592963686007264695808253964152865239443188571083361581998379876059079430760280992164033648029360420159117759317899665009919995452316255475046959393627656971819341475766265633957523711596054830194788221582206885698980581733421240774829387474956392382184149217103806575710777206630738881555463333634117752715959048067008422205033786693967260276759120854362839053925878904049479837870153276602524431725510019951843225250825658716427940793703773886331030439210455083496089510471051553406125352143841209812698956619471368849245765080438834119197527020745480828302791545421995365482602285608019072262472015028543425623717674609073304281432188512987528227249289971795958030496351623851350386219096003673202953963453325827946093577459572598299808866288946207311394474734281832383255556959022046379164115617114078467909176931319806433395357228749382397689512297410765776386924559207727345281622096957434378728478622845187419958388450664757556130312800417845854287096530710344105635036201689529651195762661746067192146352777070036399061294500281735779339988788410472801204172832570958658076780877700798211503569684899357891097724601295544204651288355719365523396908261084234941072606430852469923296586675516956215669194441560921112585298841592480892926792916975602394413349667254522557878454418912205008822289849100630080459873267683733210851466412830385016079230126128021882052725865538374417640574016257449854051020301945301660872427843760087262901296213632869253070018412415289424107241758840070627834074583598925000805374633301908613167869309259681065021051361439561906771493348980600368691963384903724067359130905202925509394670466145612973909502373805395592861923499841176838146935279497450241196212473770157144375930416583091368280576132083486533295410778771573477256923345595040490517976090806682822900062408680404518056632509896712724865021746554162532454811346718398119522577809865285360788784231217281552596917741869132127642783760553146, 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'aut_phi_ratio': 17.05, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1023, 1, 1], [3, 992, 1, 1], [11, 992, 5, 1], [31, 1056, 5, 3], [33, 992, 5, 2]], 'aut_supersolvable': False, 'aut_tex': '\\SL(2,32).C_5', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 10230, 'autcentquo_group': '163680.a', 'autcentquo_hash': 6491569111290142452, 'autcentquo_nilpotent': False, 'autcentquo_order': 163680, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SL(2,32).C_5', 'cc_stats': [[1, 1, 1], [2, 1023, 1], [3, 992, 1], [11, 992, 5], [31, 1056, 15], [33, 992, 10]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '32736.a', 'commutator_count': 1, 'commutator_label': '32736.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['32736.a'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1023, 1, 1], [3, 992, 1, 1], [11, 992, 5, 1], [31, 1056, 15, 1], [33, 992, 10, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 6330, 'exponent': 2046, 'exponents_of_order': [5, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11, 31], 'factors_of_order': [2, 3, 11, 31], 'faithful_reps': [[31, 1, 16], [32, 1, 1], [33, 1, 15]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '32736.a', 'hash': 3444694160148303414, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 2046, 'inner_gen_orders': [31, 3], 'inner_gens': [[589826, 4385], [81938, 1057]], 'inner_hash': 3444694160148303414, 'inner_nilpotent': False, 'inner_order': 32736, 'inner_split': True, 'inner_tex': '\\SL(2,32)', 'inner_used': [1, 2], 'irrC_degree': 31, 'irrQ_degree': 31, 'irrQ_dim': 31, 'irrR_degree': 31, 'irrep_stats': [[1, 1], [31, 16], [32, 1], [33, 15]], 'label': '32736.a', 'linC_count': 16, 'linC_degree': 31, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 31, 'linQ_degree_count': 1, 'linQ_dim': 31, 'linQ_dim_count': 1, 'linR_count': 16, 'linR_degree': 31, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,32)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 33, 'number_divisions': 6, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 24, 'number_subgroups': 22328, 'old_label': None, 'order': 32736, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1023], [3, 992], [11, 4960], [31, 15840], [33, 9920]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 5, 'outer_gen_orders': [5], 'outer_gen_pows': [676180], 'outer_gens': [[841627, 576880]], 'outer_group': '5.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 5, 'outer_permdeg': 5, 'outer_perms': [33], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_5', 'pc_rank': None, 'perfect': True, 'permutation_degree': 33, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [31, 1], [32, 1], [155, 1], [310, 1], [495, 1]], 'representations': {'Lie': [{'d': 2, 'q': 32, 'gens': [1057, 589826], 'family': 'SL'}, {'d': 2, 'q': 32, 'family': 'PSL'}, {'d': 2, 'q': 32, 'gens': [32770, 1057], 'family': 'PGL'}, {'d': 3, 'q': 32, 'gens': [1074791424, 1074791457, 2199024304146], 'family': 'SO'}, {'d': 2, 'q': 32, 'gens': [519691043140, 1049601], 'family': 'SU'}, {'d': 3, 'q': 32, 'family': 'PSO'}, {'d': 2, 'q': 32, 'family': 'PSU'}, {'d': 3, 'q': 32, 'gens': [1074791457, 4398047559689], 'family': 'Omega'}, {'d': 2, 'q': 32, 'family': 'PGU'}, {'d': 3, 'q': 32, 'family': 'POmega'}, {'d': 3, 'q': 32, 'family': 'CSO'}, {'d': 2, 'q': 32, 'family': 'CSU'}], 'GLFq': {'d': 2, 'q': 32, 'gens': [56480, 800633]}, 'Perm': {'d': 33, 'gens': [8306634807930607088270990526611160080, 271628086406341595119153278820940310, 246136337988397400263347478838119375]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,32)', 'transitive_degree': 33, 'wreath_data': None, 'wreath_product': False}

Column	Type
aut_label	text
centralizer	text
counter	integer
group_counter	integer
group_order	numeric
label	text
order	integer
powers	integer[]
representative	numeric
size	numeric

gps_conj_classes • Show schema

id: 174443479
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 32736, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1, 1], 'representative': 32769, 'size': 1}
id: 174443490
{'aut_label': '2A', 'centralizer': '1023.a1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 32736, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2, 2], 'representative': 870554, 'size': 1023}
id: 174443501
{'aut_label': '3A', 'centralizer': '992.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 32736, 'label': '3A', 'order': 3, 'powers': [3, 1, 3, 3, 3], 'representative': 368426, 'size': 992}
id: 174443506
{'aut_label': '11A1', 'centralizer': '992.a1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 32736, 'label': '11A1', 'order': 11, 'powers': [5, 6, 8, 1, 5], 'representative': 831747, 'size': 992}
id: 174443507
{'aut_label': '11A1', 'centralizer': '992.a1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 32736, 'label': '11A2', 'order': 11, 'powers': [7, 8, 4, 1, 7], 'representative': 304586, 'size': 992}
id: 174443508
{'aut_label': '11A1', 'centralizer': '992.a1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 32736, 'label': '11A3', 'order': 11, 'powers': [8, 5, 7, 1, 8], 'representative': 451100, 'size': 992}
id: 174443509
{'aut_label': '11A1', 'centralizer': '992.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 32736, 'label': '11A4', 'order': 11, 'powers': [6, 4, 5, 1, 6], 'representative': 880223, 'size': 992}
id: 174443510
{'aut_label': '11A1', 'centralizer': '992.a1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 32736, 'label': '11A5', 'order': 11, 'powers': [4, 7, 6, 1, 4], 'representative': 460706, 'size': 992}
id: 174443511
{'aut_label': '31A1', 'centralizer': '1056.a1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 32736, 'label': '31A1', 'order': 31, 'powers': [10, 11, 13, 19, 1], 'representative': 582357, 'size': 1056}
id: 174443480
{'aut_label': '31A1', 'centralizer': '1056.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 32736, 'label': '31A2', 'order': 31, 'powers': [12, 14, 18, 17, 1], 'representative': 507487, 'size': 1056}
id: 174443481
{'aut_label': '31A3', 'centralizer': '1056.a1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 32736, 'label': '31A3', 'order': 31, 'powers': [14, 17, 23, 10, 1], 'representative': 263814, 'size': 1056}
id: 174443482
{'aut_label': '31A1', 'centralizer': '1056.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 32736, 'label': '31A4', 'order': 31, 'powers': [16, 20, 19, 21, 1], 'representative': 339207, 'size': 1056}
id: 174443483
{'aut_label': '31A5', 'centralizer': '1056.a1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 32736, 'label': '31A5', 'order': 31, 'powers': [18, 23, 14, 15, 1], 'representative': 172602, 'size': 1056}
id: 174443484
{'aut_label': '31A3', 'centralizer': '1056.a1.a1', 'counter': 14, 'group_counter': 1, 'group_order': 32736, 'label': '31A6', 'order': 31, 'powers': [20, 21, 9, 12, 1], 'representative': 997568, 'size': 1056}
id: 174443485
{'aut_label': '31A3', 'centralizer': '1056.a1.a1', 'counter': 15, 'group_counter': 1, 'group_order': 32736, 'label': '31A7', 'order': 31, 'powers': [22, 18, 12, 23, 1], 'representative': 611642, 'size': 1056}
id: 174443486
{'aut_label': '31A1', 'centralizer': '1056.a1.a1', 'counter': 16, 'group_counter': 1, 'group_order': 32736, 'label': '31A8', 'order': 31, 'powers': [23, 15, 17, 13, 1], 'representative': 934119, 'size': 1056}
id: 174443487
{'aut_label': '31A5', 'centralizer': '1056.a1.a1', 'counter': 17, 'group_counter': 1, 'group_order': 32736, 'label': '31A9', 'order': 31, 'powers': [21, 12, 22, 14, 1], 'representative': 458406, 'size': 1056}
id: 174443488
{'aut_label': '31A5', 'centralizer': '1056.a1.a1', 'counter': 18, 'group_counter': 1, 'group_order': 32736, 'label': '31A10', 'order': 31, 'powers': [19, 9, 20, 22, 1], 'representative': 429887, 'size': 1056}
id: 174443489
{'aut_label': '31A5', 'centralizer': '1056.a1.a1', 'counter': 19, 'group_counter': 1, 'group_order': 32736, 'label': '31A11', 'order': 31, 'powers': [17, 10, 15, 11, 1], 'representative': 937941, 'size': 1056}
id: 174443491
{'aut_label': '31A3', 'centralizer': '1056.a1.a1', 'counter': 20, 'group_counter': 1, 'group_order': 32736, 'label': '31A12', 'order': 31, 'powers': [15, 13, 10, 16, 1], 'representative': 595393, 'size': 1056}
id: 174443492
{'aut_label': '31A5', 'centralizer': '1056.a1.a1', 'counter': 21, 'group_counter': 1, 'group_order': 32736, 'label': '31A13', 'order': 31, 'powers': [13, 16, 11, 20, 1], 'representative': 990321, 'size': 1056}
id: 174443493
{'aut_label': '31A3', 'centralizer': '1056.a1.a1', 'counter': 22, 'group_counter': 1, 'group_order': 32736, 'label': '31A14', 'order': 31, 'powers': [11, 19, 16, 9, 1], 'representative': 189519, 'size': 1056}
id: 174443494
{'aut_label': '31A1', 'centralizer': '1056.a1.a1', 'counter': 23, 'group_counter': 1, 'group_order': 32736, 'label': '31A15', 'order': 31, 'powers': [9, 22, 21, 18, 1], 'representative': 340328, 'size': 1056}
id: 174443495
{'aut_label': '33A1', 'centralizer': '992.a1.a1', 'counter': 24, 'group_counter': 1, 'group_order': 32736, 'label': '33A1', 'order': 33, 'powers': [25, 4, 27, 3, 25], 'representative': 461814, 'size': 992}
id: 174443496
{'aut_label': '33A1', 'centralizer': '992.a1.a1', 'counter': 25, 'group_counter': 1, 'group_order': 32736, 'label': '33A2', 'order': 33, 'powers': [26, 5, 30, 3, 26], 'representative': 185506, 'size': 992}
id: 174443497
{'aut_label': '33A1', 'centralizer': '992.a1.a1', 'counter': 26, 'group_counter': 1, 'group_order': 32736, 'label': '33A4', 'order': 33, 'powers': [29, 7, 31, 3, 29], 'representative': 856943, 'size': 992}
id: 174443498
{'aut_label': '33A5', 'centralizer': '992.a1.a1', 'counter': 27, 'group_counter': 1, 'group_order': 32736, 'label': '33A5', 'order': 33, 'powers': [30, 8, 29, 3, 30], 'representative': 363615, 'size': 992}
id: 174443499
{'aut_label': '33A5', 'centralizer': '992.a1.a1', 'counter': 28, 'group_counter': 1, 'group_order': 32736, 'label': '33A7', 'order': 33, 'powers': [32, 7, 25, 3, 32], 'representative': 431316, 'size': 992}
id: 174443500
{'aut_label': '33A1', 'centralizer': '992.a1.a1', 'counter': 29, 'group_counter': 1, 'group_order': 32736, 'label': '33A8', 'order': 33, 'powers': [33, 6, 28, 3, 33], 'representative': 31388, 'size': 992}
id: 174443502
{'aut_label': '33A5', 'centralizer': '992.a1.a1', 'counter': 30, 'group_counter': 1, 'group_order': 32736, 'label': '33A10', 'order': 33, 'powers': [31, 4, 33, 3, 31], 'representative': 320948, 'size': 992}
id: 174443503
{'aut_label': '33A5', 'centralizer': '992.a1.a1', 'counter': 31, 'group_counter': 1, 'group_order': 32736, 'label': '33A13', 'order': 33, 'powers': [28, 5, 24, 3, 28], 'representative': 833199, 'size': 992}
id: 174443504
{'aut_label': '33A5', 'centralizer': '992.a1.a1', 'counter': 32, 'group_counter': 1, 'group_order': 32736, 'label': '33A14', 'order': 33, 'powers': [27, 6, 26, 3, 27], 'representative': 183171, 'size': 992}
id: 174443505
{'aut_label': '33A1', 'centralizer': '992.a1.a1', 'counter': 33, 'group_counter': 1, 'group_order': 32736, 'label': '33A16', 'order': 33, 'powers': [24, 8, 32, 3, 24], 'representative': 43414, 'size': 992}

Column	Type
cdim	integer
counter	smallint
faithful	boolean
group	text
group_order	numeric
image	text
label	text
multiplicity	smallint
nt	integer[]
qdim	integer
qvalues	integer[]
schur_index	smallint

gps_qchar • Show schema

id: 18078165
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '32736.a', 'group_order': 32736, 'image': None, 'label': '32736.a.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 18078166
{'cdim': 31, 'counter': 2, 'faithful': True, 'group': '32736.a', 'group_order': 32736, 'image': None, 'label': '32736.a.31a', 'multiplicity': 1, 'nt': [992, 0], 'qdim': 31, 'qvalues': [31, -1, 1, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 18078169
{'cdim': 32, 'counter': 5, 'faithful': True, 'group': '32736.a', 'group_order': 32736, 'image': None, 'label': '32736.a.32a', 'multiplicity': 1, 'nt': [33, 40], 'qdim': 32, 'qvalues': [32, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 18078167
{'cdim': 31, 'counter': 3, 'faithful': True, 'group': '32736.a', 'group_order': 32736, 'image': None, 'label': '32736.a.31b', 'multiplicity': 5, 'nt': [992, 0], 'qdim': 155, 'qvalues': [155, -5, -10, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 18078168
{'cdim': 31, 'counter': 4, 'faithful': True, 'group': '32736.a', 'group_order': 32736, 'image': None, 'label': '32736.a.31c', 'multiplicity': 10, 'nt': [992, 0], 'qdim': 310, 'qvalues': [310, -10, 10, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 18078170
{'cdim': 33, 'counter': 6, 'faithful': True, 'group': '32736.a', 'group_order': 32736, 'image': None, 'label': '32736.a.33a', 'multiplicity': 15, 'nt': [496, 0], 'qdim': 495, 'qvalues': [495, 15, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

Column	Type
center	text
center_index	numeric
center_order	numeric
counter	smallint
cyclotomic_n	integer
dim	integer
faithful	boolean
field	numeric[]
group	text
group_counter	integer
group_order	numeric
image	text
image_isoclass	text
image_order	numeric
indicator	smallint
kernel	text
kernel_order	numeric
label	text
nt	integer[]
q_character	text
values	jsonb

gps_char • Show schema

id: 39151769
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 32736, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 32736, 'label': '32736.a.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 39151780
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 2, 'cyclotomic_n': 1, 'dim': 31, 'faithful': True, 'field': [0, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31a', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 39151791
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 3, 'cyclotomic_n': 11, 'dim': 31, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31b1', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
id: 39151796
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 4, 'cyclotomic_n': 11, 'dim': 31, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31b2', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]]]}
id: 39151797
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 5, 'cyclotomic_n': 11, 'dim': 31, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31b3', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[-2, 0]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]]]}
id: 39151798
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 6, 'cyclotomic_n': 11, 'dim': 31, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31b4', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[-2, 0]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]]]}
id: 39151799
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 7, 'cyclotomic_n': 11, 'dim': 31, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31b5', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[-2, 0]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]]]}
id: 39151800
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 8, 'cyclotomic_n': 33, 'dim': 31, 'faithful': True, 'field': [1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31c1', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 12], [-1, -12]], [[-1, 15], [-1, -15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[-1, 8], [-1, -8]], [[-1, 10], [-1, -10]], [[-1, 13], [-1, -13]], [[-1, 14], [-1, -14]], [[-1, 16], [-1, -16]]]}
id: 39151777
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 33, 'dim': 31, 'faithful': True, 'field': [1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31c10', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[-1, 15], [-1, -15]], [[-1, 3], [-1, -3]], [[-1, 12], [-1, -12]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 16], [-1, -16]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 14], [-1, -14]], [[-1, 13], [-1, -13]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[-1, 7], [-1, -7]], [[-1, 8], [-1, -8]]]}
id: 39151801
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 9, 'cyclotomic_n': 33, 'dim': 31, 'faithful': True, 'field': [1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31c2', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 12], [-1, -12]], [[-1, 15], [-1, -15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 10], [-1, -10]], [[-1, 13], [-1, -13]], [[-1, 7], [-1, -7]], [[-1, 16], [-1, -16]], [[-1, 4], [-1, -4]], [[-1, 14], [-1, -14]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 8], [-1, -8]], [[-1, 5], [-1, -5]]]}
id: 39151770
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id: 39151771
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id: 39151772
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id: 39151773
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 33, 'dim': 31, 'faithful': True, 'field': [1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31c6', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[-1, 9], [-1, -9]], [[-1, 15], [-1, -15]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 14], [-1, -14]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 13], [-1, -13]], [[-1, 8], [-1, -8]], [[-1, 16], [-1, -16]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]]]}
id: 39151774
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 33, 'dim': 31, 'faithful': True, 'field': [1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31c7', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[-1, 12], [-1, -12]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 15], [-1, -15]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[-1, 16], [-1, -16]], [[-1, 13], [-1, -13]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 14], [-1, -14]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]]]}
id: 39151775
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 33, 'dim': 31, 'faithful': True, 'field': [1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31c8', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[-1, 12], [-1, -12]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 15], [-1, -15]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 7], [-1, -7]], [[-1, 14], [-1, -14]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 16], [-1, -16]], [[-1, 10], [-1, -10]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[-1, 1], [-1, -1]], [[-1, 13], [-1, -13]]]}
id: 39151776
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 33, 'dim': 31, 'faithful': True, 'field': [1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.31c9', 'nt': [992, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[-1, 15], [-1, -15]], [[-1, 3], [-1, -3]], [[-1, 12], [-1, -12]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[-1, 13], [-1, -13]], [[-1, 8], [-1, -8]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 16], [-1, -16]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 14], [-1, -14]]]}
id: 39151778
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 1, 'dim': 32, 'faithful': True, 'field': [0, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.32a', 'nt': [33, 40], 'q_character': None, 'values': [[[32, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 39151779
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a1', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 15], [1, -15]], [[1, 1], [1, -1]], [[1, 14], [1, -14]], [[1, 2], [1, -2]], [[1, 13], [1, -13]], [[1, 3], [1, -3]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[1, 11], [1, -11]], [[1, 5], [1, -5]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 7], [1, -7]], [[1, 8], [1, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151789
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a10', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 12], [1, -12]], [[1, 13], [1, -13]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 11], [1, -11]], [[1, 14], [1, -14]], [[1, 8], [1, -8]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 10], [1, -10]], [[1, 15], [1, -15]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151790
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a11', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 10], [1, -10]], [[1, 15], [1, -15]], [[1, 11], [1, -11]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 9], [1, -9]], [[1, 14], [1, -14]], [[1, 12], [1, -12]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 8], [1, -8]], [[1, 13], [1, -13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151792
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a12', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[1, 12], [1, -12]], [[1, 15], [1, -15]], [[1, 11], [1, -11]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[1, 14], [1, -14]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151793
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a13', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 12], [1, -12]], [[1, 15], [1, -15]], [[1, 13], [1, -13]], [[1, 10], [1, -10]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 8], [1, -8]], [[1, 11], [1, -11]], [[1, 14], [1, -14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151794
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a14', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 8], [1, -8]], [[1, 10], [1, -10]], [[1, 12], [1, -12]], [[1, 14], [1, -14]], [[1, 15], [1, -15]], [[1, 13], [1, -13]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151795
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a15', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 8], [1, -8]], [[1, 9], [1, -9]], [[1, 10], [1, -10]], [[1, 11], [1, -11]], [[1, 12], [1, -12]], [[1, 13], [1, -13]], [[1, 14], [1, -14]], [[1, 15], [1, -15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151781
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a2', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 14], [1, -14]], [[1, 3], [1, -3]], [[1, 11], [1, -11]], [[1, 6], [1, -6]], [[1, 8], [1, -8]], [[1, 9], [1, -9]], [[1, 5], [1, -5]], [[1, 12], [1, -12]], [[1, 2], [1, -2]], [[1, 15], [1, -15]], [[1, 1], [1, -1]], [[1, 13], [1, -13]], [[1, 4], [1, -4]], [[1, 10], [1, -10]], [[1, 7], [1, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151782
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a3', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 13], [1, -13]], [[1, 5], [1, -5]], [[1, 8], [1, -8]], [[1, 10], [1, -10]], [[1, 3], [1, -3]], [[1, 15], [1, -15]], [[1, 2], [1, -2]], [[1, 11], [1, -11]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 12], [1, -12]], [[1, 1], [1, -1]], [[1, 14], [1, -14]], [[1, 4], [1, -4]], [[1, 9], [1, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151783
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a4', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12], [1, -12]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[1, 14], [1, -14]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 15], [1, -15]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[1, 11], [1, -11]], [[1, 1], [1, -1]], [[1, 13], [1, -13]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151784
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a5', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[1, 2], [1, -2]], [[1, 13], [1, -13]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 15], [1, -15]], [[1, 5], [1, -5]], [[1, 6], [1, -6]], [[1, 14], [1, -14]], [[1, 3], [1, -3]], [[1, 8], [1, -8]], [[1, 12], [1, -12]], [[1, 1], [1, -1]], [[1, 10], [1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151785
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a6', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 10], [1, -10]], [[1, 11], [1, -11]], [[1, 1], [1, -1]], [[1, 9], [1, -9]], [[1, 12], [1, -12]], [[1, 2], [1, -2]], [[1, 8], [1, -8]], [[1, 13], [1, -13]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 14], [1, -14]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 15], [1, -15]], [[1, 5], [1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151786
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a7', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 14], [1, -14]], [[1, 8], [1, -8]], [[1, 1], [1, -1]], [[1, 10], [1, -10]], [[1, 12], [1, -12]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 15], [1, -15]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 11], [1, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151787
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a8', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[1, 15], [1, -15]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 9], [1, -9]], [[1, 14], [1, -14]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[1, 13], [1, -13]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 11], [1, -11]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 39151788
{'center': '32736.a1.a1', 'center_index': 32736, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 31, 'dim': 33, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '32736.a', 'group_counter': 1, 'group_order': 32736, 'image': None, 'image_isoclass': '32736.a', 'image_order': 32736, 'indicator': 1, 'kernel': '32736.a1.a1', 'kernel_order': 1, 'label': '32736.a.33a9', 'nt': [496, 0], 'q_character': None, 'values': [[[33, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 7], [1, -7]], [[1, 14], [1, -14]], [[1, 10], [1, -10]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 11], [1, -11]], [[1, 13], [1, -13]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 8], [1, -8]], [[1, 15], [1, -15]], [[1, 9], [1, -9]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 12], [1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
ambient	text
ambient_counter	integer
ambient_order	numeric
ambient_tex	text
central	boolean
central_factor	boolean
centralizer_order	numeric
characteristic	boolean
core_order	numeric
counter	integer
cyclic	boolean
direct	boolean
hall	numeric
label	text
maximal	boolean
maximal_normal	boolean
metabelian	boolean
metacyclic	boolean
minimal	boolean
minimal_normal	boolean
nilpotent	boolean
normal	boolean
old_label	text
outer_equivalence	boolean
perfect	boolean
proper	boolean
quotient	text
quotient_Agroup	boolean
quotient_abelian	boolean
quotient_cyclic	boolean
quotient_hash	bigint
quotient_metabelian	boolean
quotient_nilpotent	boolean
quotient_order	numeric
quotient_simple	boolean
quotient_solvable	boolean
quotient_supersolvable	boolean
quotient_tex	text
simple	boolean
solvable	boolean
special_labels	text[]
split	boolean
standard_generators	boolean
stem	boolean
subgroup	text
subgroup_hash	bigint
subgroup_order	numeric
subgroup_tex	text
supersolvable	boolean
sylow	smallint

gps_subgroup_search • Show schema

id: 269049353
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 32736, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2046, 'label': '32736.a.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_1', 'simple': True, 'solvable': False, 'special_labels': ['D', 'S', 'PC', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32736.a', 'subgroup_hash': 3444694160148303414, 'subgroup_order': 32736, 'subgroup_tex': '\\SL(2,32)', 'supersolvable': False, 'sylow': 0}
id: 269049364
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 62, 'label': '32736.a.33.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '33.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '992.194', 'subgroup_hash': 194, 'subgroup_order': 992, 'subgroup_tex': 'F_{32}', 'supersolvable': False, 'sylow': 0}
id: 269049370
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.496.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '496.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 496, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.3', 'subgroup_hash': 3, 'subgroup_order': 66, 'subgroup_tex': 'D_{33}', 'supersolvable': True, 'sylow': 0}
id: 269049371
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.528.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '528.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '62.1', 'subgroup_hash': 1, 'subgroup_order': 62, 'subgroup_tex': 'D_{31}', 'supersolvable': True, 'sylow': 0}
id: 269049372
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 33, 'characteristic': False, 'core_order': 1, 'counter': 5, 'cyclic': True, 'direct': None, 'hall': 33, 'label': '32736.a.992.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '992.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 992, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
id: 269049373
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '32736.a.1023.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1023.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1023, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 2}
id: 269049374
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 31, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': True, 'direct': None, 'hall': 31, 'label': '32736.a.1056.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1056.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1056, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '31.1', 'subgroup_hash': 1, 'subgroup_order': 31, 'subgroup_tex': 'C_{31}', 'supersolvable': True, 'sylow': 31}
id: 269049375
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.1488.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1488.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1488, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
id: 269049376
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.2046.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2046.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2046, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 269049354
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 33, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': True, 'direct': None, 'hall': 11, 'label': '32736.a.2976.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2976.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2976, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
id: 269049355
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.4092.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4092.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4092, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 269049356
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.4092.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4092.a1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4092, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 269049357
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.4092.a1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4092.a1.a3', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4092, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 269049358
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.4092.a1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4092.a1.a4', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4092, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 269049359
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.4092.a1.a5', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4092.a1.a5', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4092, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 269049360
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.5456.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5456.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5456, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 269049361
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.8184.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8184.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 269049362
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.8184.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8184.a1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 269049363
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.8184.a1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8184.a1.a3', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 269049365
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.8184.a1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8184.a1.a4', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 269049366
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32736.a.8184.a1.a5', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8184.a1.a5', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 269049367
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 33, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '32736.a.10912.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10912.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10912, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
id: 269049368
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '32736.a.16368.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16368.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 269049369
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32736.a', 'ambient_counter': 1, 'ambient_order': 32736, 'ambient_tex': '\\SL(2,32)', 'central': True, 'central_factor': False, 'centralizer_order': 32736, 'characteristic': True, 'core_order': 1, 'counter': 24, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '32736.a.32736.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32736.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '32736.a', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3444694160148303414, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 32736, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': None, 'quotient_tex': '\\SL(2,32)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'Phi', 'R', 'U0', 'C1'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

Column	Type
ambient	text
aut_centralizer_order	numeric
aut_label	text
aut_quo_index	numeric
aut_stab_index	numeric
aut_weyl_group	text
aut_weyl_index	numeric
centralizer	text
complements	text[]
conjugacy_class_count	numeric
contained_in	text[]
contains	text[]
core	text
coset_action_label	text
count	numeric
diagramx	smallint[]
generators	numeric[]
label	text
mobius_quo	bigint
mobius_sub	bigint
normal_closure	text
normal_contained_in	text[]
normal_contains	text[]
normalizer	text
old_label	text
projective_image	text
quotient_action_image	text
quotient_action_kernel	text
quotient_action_kernel_order	numeric
quotient_fusion	jsonb
short_label	text
subgroup_fusion	integer[]
weyl_group	text

gps_subgroup_data • Show schema

id: 269049353
{'ambient': '32736.a', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32736.a1.a1', 'complements': ['32736.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['33.a1.a1', '496.a1.a1', '528.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3348, 5000, 8478, 5000, 3815, 5000, 2226, 5000], 'generators': [879803, 567280], 'label': '32736.a.1.a1.a1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['32736.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '32736.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13122.bd'}
id: 269049354
{'ambient': '32736.a', 'aut_centralizer_order': None, 'aut_label': '2976.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '992.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['992.a1.a1', '1488.a1.a1'], 'contains': ['32736.a1.a1'], 'core': '32736.a1.a1', 'coset_action_label': None, 'count': 496, 'diagramx': [8929, -1, 574, -1, 5032, -1, 7120, -1], 'generators': [755474], 'label': '32736.a.2976.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '496.a1.a1', 'old_label': '2976.a1.a1', 'projective_image': '32736.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2976.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 269049355
{'ambient': '32736.a', 'aut_centralizer_order': None, 'aut_label': '4092.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1023.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2046.a1.a1'], 'contains': ['8184.a1.a1', '8184.a1.a2', '8184.a1.a3', '8184.a1.a4', '8184.a1.a5'], 'core': '32736.a1.a1', 'coset_action_label': None, 'count': 1023, 'diagramx': [2478, -1, 4325, -1, 3004, -1, 1036, -1], 'generators': [23712, 187013, 512623], 'label': '32736.a.4092.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1023.a1.a1', 'old_label': '4092.a1.a1', 'projective_image': '32736.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4092.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 269049356
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id: 269049357
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id: 269049358
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id: 269049359
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id: 269049360
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id: 269049361
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id: 269049362
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id: 269049363
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id: 269049364
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id: 269049365
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id: 269049366
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id: 269049367
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id: 269049368
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id: 269049369
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id: 269049370
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id: 269049371
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id: 269049372
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id: 269049373
{'ambient': '32736.a', 'aut_centralizer_order': None, 'aut_label': '1023.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1023.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['33.a1.a1'], 'contains': ['2046.a1.a1'], 'core': '32736.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [1629, -1, 6809, -1, 3815, -1, 2843, -1], 'generators': [207718, 23712, 675188, 187013, 963709], 'label': '32736.a.1023.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '1023.a1.a1', 'projective_image': '32736.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1023.a1.a1', 'subgroup_fusion': None, 'weyl_group': '31.1'}
id: 269049374
{'ambient': '32736.a', 'aut_centralizer_order': None, 'aut_label': '1056.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1056.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['33.a1.a1', '528.a1.a1'], 'contains': ['32736.a1.a1'], 'core': '32736.a1.a1', 'coset_action_label': None, 'count': 528, 'diagramx': [1071, -1, 9791, -1, 1660, -1, 522, -1], 'generators': [365860], 'label': '32736.a.1056.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '528.a1.a1', 'old_label': '1056.a1.a1', 'projective_image': '32736.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1056.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 269049375
{'ambient': '32736.a', 'aut_centralizer_order': None, 'aut_label': '1488.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32736.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['496.a1.a1'], 'contains': ['2976.a1.a1', '16368.a1.a1'], 'core': '32736.a1.a1', 'coset_action_label': None, 'count': 1488, 'diagramx': [6094, -1, 1553, -1, 5032, -1, 7120, -1], 'generators': [797592, 755474], 'label': '32736.a.1488.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1488.a1.a1', 'old_label': '1488.a1.a1', 'projective_image': '32736.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1488.a1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
id: 269049376
{'ambient': '32736.a', 'aut_centralizer_order': None, 'aut_label': '2046.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1023.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1023.a1.a1'], 'contains': ['4092.a1.a1', '4092.a1.a2', '4092.a1.a3', '4092.a1.a4', '4092.a1.a5'], 'core': '32736.a1.a1', 'coset_action_label': None, 'count': 1023, 'diagramx': [2478, -1, 6072, -1, 3181, -1, 2843, -1], 'generators': [207718, 23712, 187013, 963709], 'label': '32736.a.2046.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1023.a1.a1', 'old_label': '2046.a1.a1', 'projective_image': '32736.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2046.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.